This application is a United States counterpart to and claims the benefit of the filing date of French Application No. 98/09578 dated Jul. 23, 1998, which is herein incorporated by reference.
The present invention generally relates to the field of QPSK (quadrature phase-shift keying) demodulators for restoring two binary signals carried by two carriers of same frequency but in phase quadrature. The present invention more specifically relates to an estimator of the error of the frequency on which a phase-locked loop of the demodulator is set.
FIG. 1 shows, in the form of a constellation, couples of values, or symbols, corresponding to the successive values of the two binary signals restored by a demodulator. This constellation shows points, each of which has as coordinates values I and Q of the two binary signals at a given time. Theoretically, the points coincide with points P1 to P4 of respective coordinates (1, 1), (xe2x88x921, 1), (xe2x88x921, xe2x88x921) and (1, xe2x88x921).
However, as shown in the first quadrant of the constellation, points which should coincide with point P1 form a cloud of points around point P1 due to various errors and to noise in the transmission.
A QPSK demodulator is generally formed of a phase-locked loop (PLL) for setting the frequency of a local oscillator on the carrier frequency by an analysis of the constellation points. To filter the noise, the PLL has a very small bandwidth, on the order of one thousandth of the transmission frequency, or symbol frequency, of the binary signals. Thereby, the PLL also has a narrow capture range, which further decreases when the noise increases. This range is on the order of 0.5% of the symbol frequency with a 3-dB signal-to-noise ratio. The carrier frequency is generally not very well known and the offset can be several times the symbol frequency. Thus, if no specific measures are taken, the PLL does not succeed in setting on the carrier frequency.
When the frequency of the PLL is poorly adjusted, the constellation of received points rotates, as illustrated by arrows in FIG. 1, at a speed equal to the frequency error.
A first conventional solution to find a frequency within the capture range of the PLL consists of adjusting the PLL frequency on successive selected values until a locking of the PLL is detected. A PLL locking detection is a relatively slow operation which requires analyzing a large number of symbols for each tested frequency. The number of symbols to be analyzed increases with noise. In satellite transmissions, a signal-to-noise ratio as small as 3 dB is generally tolerated. In this case, several tens of thousands of symbols have to be analyzed to detect the locking, which considerably slows down the rate of the successive frequency tests and thus the speed at which the demodulator is set on the carrier frequency.
Other solutions use a frequency error estimator for bringing the demodulator frequency in a single attempt within its capture range. An example of frequency estimator is described in the paper entitled xe2x80x9cFrequency Detectors for PLL Acquisition in Timing and Carrier Recoveryxe2x80x9d by David G. Messerschmitt, IEEE Transactions on Communications, Vol. 27, No. 9, September 1979.
This estimator exploits given properties of the signal and provides a value which is in principle proportional to the frequency error. However, this type of estimator provides the position of the gravity center of the signal spectrum and thus only is operative if this spectrum is symmetrical. In most real situations, the spectrum is not always symmetrical due to the characteristics of the signal transmission, which fluctuate with respect to the desired theoretical characteristics. Thus, the frequency value provided by the estimator fluctuates in practice by a few hundredths of the symbol frequency and often falls outside the PLL capture range.
A frequency error detector is described in the paper entitled xe2x80x9cNew Phase and Frequency Detectors for Carrier Recovery in PSK and QAM systemsxe2x80x9d, by Hikmet Sari and Saxc3xafd Moridi, IEEE Transactions on Communications, Vol. 36, No. 9, September 1988. This detector analyzes the variation of the phase error of the PLL. Indeed, in the case of a frequency error, the phase varies linearly in time, modulo xcfx80/2 in a QPSK demodulator. In the absence of noise, the phase has a sawtooth-shaped variation between xe2x88x92xcfx80/4 and xcfx80/4, and the frequency corresponds to the slope of each of the ramps of the sawtooth. The system provides the measured phase error when it is included between a positive and a negative threshold, and provides the last value measured between these thresholds otherwise. However, in the presence of a strong noise, the points of each ramp are superposed to random errors which can often exceed xcfx80/4 in absolute value. It is then practically impossible to have a reliable result.
An object of the present invention is to provide an estimator of the frequency error of a QPSK demodulator, which is particularly reliable, even in the presence of strong noise. This object is achieved by a method for estimating the frequency error of a demodulator for restoring two binary signals carried on two carriers of same frequency but in phase quadrature, including the steps of forming vectors having as components the successive couples of values of the two binary signals; applying to each vector a transform which multiplies by four its angle at least when it is equal to a multiple of xcfx80/4 and which substantially preserves its module; and calculating the average of the transformed vectors.
According to an embodiment of the present invention, the transform is a rotation by four times the vector angle.
According to an embodiment of the present invention, the frequency error is provided by calculating the derivative of the angle of the average vector.
According to an embodiment of the present invention, the derivative is provided in the form of a difference, modulo xcfx80/2, of two successive angle values.
According to an embodiment of the present invention, the transform is a piecewise linear transform which makes correspond to each vector an image vector located substantially in the same quadrant of the image plane as an image vector obtained by multiplying by four the vector angle.
According to an embodiment of the present invention, a phase of 0 is assigned to the image vectors located in the second and third quadrants of the image plane, a phase of +1 is assigned to the image vectors located in the first quadrant, and a phase of xe2x88x921 is assigned to the image vectors located in the fourth quadrant, a frequency error information being provided by the difference of the phase values assigned to the current image vector and to the preceding image vector, which difference is provided modulo 2 if it is positive, and modulo xe2x88x922 if negative.